Roots of Polynomials Flashcards
1
Q
ax²+bx+c=0
α+β=?
αβ=?
A
α+β=-b/a
αβ=c/a
2
Q
ax³+bx²+cx+d=0
α+β+γ=
αy+βγ+αγ=
αβγ=
A
α+β+γ=-b/a
αβ+βγ+αγ=c/a
αβγ=-d/a
3
Q
ax⁴+bx³+cx²+dx+e=0
α+β+γ+δ=
αβ+αγ+αδ+βγ+βδ+γδ=
αβγ+αβδ+αγδ+βγδ=
αβγδ=
A
α+β+γ+δ=-b/a
αβ+αγ+αδ+βγ+βδ+γδ=c/a
αβγ+αβδ+αγδ+βγδ=-d/a
αβγδ=e/a
4
Q
(1/α)+(1/β)=
A
(α+β)/αβ
5
Q
(1/α)+(1/β)+(1/γ)=
A
(αβ+βδ+αγ)/αβγ
6
Q
(1/α)+(1/β)+(1/γ)+(1/δ)=
A
(αβγ+αβδ+αγδ+βγδ)/αβγδ
7
Q
α²+β²=
A
(α+β)²-2αβ
8
Q
α³+β³=
A
(α+β)³-3αβ(α+β)
9
Q
α²+β²+γ²=
A
(α+β+γ)²-2(αβ+βδ+αγ)
10
Q
α²+β²+γ²+δ²=
A
(α+β+γ+δ)²-2(αβ+αγ+αδ+βγ+βδ+γδ)
11
Q
α³+β³+γ³=
A
(α+β+γ)³-3(α+β+γ)(αβ+βδ+αγ)+3αβγ
12
Q
If the roots are transformed by 2n, you…
A
Set w=2x, then subsitute
13
Q
If the roots are transformed by f(x), you…
A
Set w=f(x), then rearrange and substitute
